drain the system completely and flush it out, getting rid of any muck in there.
Make sure belt to water pump is not slack.
Take the thermostat out and drop it into a bowl of boiling water to see if it operates, if not a new one. For the cost I'd put a new one in anyway.
When you refilled, run the engine and squeeze the rad hoses to get all the air out with the cap off. Make sure you have the blue rated expansion tank cap too. Remember to re check level and refit cap.
No temp light can be a poor connection on the clocks, so putting a couple of turns of leccy tape around the stub where the blue foil fits over helps with better contact. In fact it helps with a lot of clock faults inc flashing temp light etc etc.
Also clean the copper contacts carefully too.
There are 2 sensors that operate the light one in the expansion tank for low level fluid warning plus one on the coolant flange to show over heating.
I put a new red spade connector on the wire and a new sensor in from GSF about a fiver???